Question

Find the total area for the regular pyramid.

Answer 1

Answer:

• Option B

Step-by-step explanation:

Given is the hexagonal pyramid.

We know the radius of the base is same as its side.

Find the base area:

• A = 3√3/2a²
• A = 3√3/2*6² = 54√3

Given the height and radius, find the side of the lateral triangular faces:

• $\sqrt{8^2+6^2} =\sqrt{100} =10$

Each of 6 triangles have sides 10, 10 and 6 units.

Find the area using heron's formula:

• s = P/2 = (10*2 + 6)/2 = 13
• s - a = s - b = 13 - 10 = 3
• s - c = 13 - 6 = 7
• $A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{13*3*3*7} =3\sqrt{91}$

Total surface area:

• $S = 6*3\sqrt{91}+54\sqrt{3} =18\sqrt{91}+54\sqrt{3}$

Correct choice is B